Ponzi Game in OLG Model with Endogenous Growth and Productive Government Spending

Barro's model is an AK model, and there cannot be dynamic ineffciency since the social yield of the capital is higher than the growth rate. But it may be that the private yield and thus the interest rate are lower than the growth rate. One can thus have a Ponzi game and the government can allow a permanent roll-over of debt. However we show that in this model since the capital is under-accumulated, playing a Ponzi game produces a crowding-out of capital and reduces the growth rate and welfare. The practical message of this article is that even when the interest rate is lower than the growth rate, the national debt is not necessarily a Pareto improvement because it generates a crowding-out of capital which produces learning-by-doing